Presentation is loading. Please wait.

Presentation is loading. Please wait.

Regression Analysis with MATLAB. MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');

Published byCharlotte Campbell Modified over 9 years ago

Similar presentations

Presentation on theme: "Regression Analysis with MATLAB. MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');"— Presentation transcript:

1 Regression Analysis with MATLAB

2 MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');

3 MATLAB codes

4 Read the data into workspace of MATLAB y=data(:,3); x(:,2)=data(:,2); x(:,1)=1; n=size(x,1);

5 MATLAB codes Read the data into workspace of MATLAB

6 MATLAB codes Computation steps

7 MATLAB codes Calculate Beta and Q beta=inv(x'*x)*x'*y; Q=(y-x*beta)'*(y-x*beta);

8 MATLAB codes Calculate Beta and Q

9 MATLAB codes Calculate H, yhat, sigma square and covariance of beta h=x*inv((x'*x))*x'; yhat=h*y; sigma2=Q/(n-2); covbeta=sigma2*inv(x'*x);

10 MATLAB codes Calculate H, yhat, sigma square and covariance of beta

11 MATLAB codes Calculate H, yhat, sigma square and covariance of beta

12 MATLAB codes Define Dn yi=ones(n,1); i=eye(n); D=i-(1/n)*yi*yi';

13 MATLAB codes Define Dn

14 MATLAB codes Compute SStotal and SSreg SStotal=y'*D*y; SSreg=yhat'*D*yhat;

15 MATLAB codes Compute SStotal and SSreg

16 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 Residual0.863 Total111.917

17 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917

18 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 N=? Sigma square=? R square=?

19 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 N=12 Sigma square= 0.0863 R square=0.550

20 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 b1=? b0=? Var(b1)=? Var(b0)=? X bar=49.3333 Y bar=3.5 Sxx=306.67 Sxy=17.97

21 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 b1=0.059 b0=0.003 Var(b1)= 0.000281 Var(b0)= 0.69208 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

22 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 t(b1)=? X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

23 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 t=3.493 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

24 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 Var(y-hat)=?, at x=45 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

25 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 Var(y-hat)=0.012476, at x=45 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

26 That’s all

Download ppt "Regression Analysis with MATLAB. MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');"

Similar presentations

Regression. Lines y=mx+b y=mx+b m = slope of the line; how steep it is m = slope of the line; how steep it is b = y-intercept of the line; where the line.

Regression. Lines y=mx+b y=mx+b m = slope of the line; how steep it is m = slope of the line; how steep it is b = y-intercept of the line; where the line.
1 Regression as Moment Structure. 2 Regression Equation Y =  X + v Observable Variables Y z = X Moment matrix  YY  YX  =  YX  XX Moment structure.

1 Regression as Moment Structure. 2 Regression Equation Y =  X + v Observable Variables Y z = X Moment matrix  YY  YX  =  YX  XX Moment structure.
Topic 12: Multiple Linear Regression

Topic 12: Multiple Linear Regression
Analysis of Variance (ANOVA). Hypothesis H 0 :  i =  G H 1 :  i | (  i   G ) Logic S 2 within = error variability S 2 between = error variability.

Analysis of Variance (ANOVA). Hypothesis H 0 :  i =  G H 1 :  i | (  i   G ) Logic S 2 within = error variability S 2 between = error variability.
Linear regression and correlation

Linear regression and correlation
Econ 140 Lecture 81 Classical Regression II Lecture 8.

Econ 140 Lecture 81 Classical Regression II Lecture 8.
Classical Regression III

Classical Regression III
CORRELATION AND SIMPLE LINEAR REGRESSION - Revisited Ref: Cohen, Cohen, West, & Aiken (2003), ch. 2.

CORRELATION AND SIMPLE LINEAR REGRESSION - Revisited Ref: Cohen, Cohen, West, & Aiken (2003), ch. 2.
Analysis – Regression The ANOVA through regression approach is still the same, but expanded to include all IVs and the interaction The number of orthogonal.

Analysis – Regression The ANOVA through regression approach is still the same, but expanded to include all IVs and the interaction The number of orthogonal.
ANOVA Types of Variation. Variation between Groups Weighted sum of variances between sample mean and overall mean Large  factor affects system Small.

ANOVA Types of Variation. Variation between Groups Weighted sum of variances between sample mean and overall mean Large  factor affects system Small.
Type of Measurement Differences between three or more independent groups Interval or ratio One-way ANOVA.

Type of Measurement Differences between three or more independent groups Interval or ratio One-way ANOVA.
Lesson #23 Analysis of Variance. In Analysis of Variance (ANOVA), we have: H 0 :  1 =  2 =  3 = … =  k H 1 : at least one  i does not equal the others.

Lesson #23 Analysis of Variance. In Analysis of Variance (ANOVA), we have: H 0 :  1 =  2 =  3 = … =  k H 1 : at least one  i does not equal the others.
Dr. Michael R. Hyman, NMSU Analysis of Variance (ANOVA) (Click icon for audio)

Dr. Michael R. Hyman, NMSU Analysis of Variance (ANOVA) (Click icon for audio)
Analysis of Variance: Some Review and Some New Ideas

Analysis of Variance: Some Review and Some New Ideas
Introduction to Regression Analysis. Two Purposes Explanation –Explain (or account for) the variance in a variable (e.g., explain why children’s test.

Introduction to Regression Analysis. Two Purposes Explanation –Explain (or account for) the variance in a variable (e.g., explain why children’s test.
Linear Regression When looking for a linear relationship between two sets of data we can plot what is known as a scatter diagram. x y Looking at the graph.

Linear Regression When looking for a linear relationship between two sets of data we can plot what is known as a scatter diagram. x y Looking at the graph.
Completing the ANOVA From the Summary Statistics.

Completing the ANOVA From the Summary Statistics.
Lecture 9: ANOVA tables F-tests BMTRY 701 Biostatistical Methods II.

Lecture 9: ANOVA tables F-tests BMTRY 701 Biostatistical Methods II.
Regression Regression relationship = trend + scatter

Regression Regression relationship = trend + scatter
1 Statistical Analysis Professor Lynne Stokes Department of Statistical Science Lecture 8 Analysis of Variance.

1 Statistical Analysis Professor Lynne Stokes Department of Statistical Science Lecture 8 Analysis of Variance.

Similar presentations

Ads by Google